To make adaptive choices, humans need to estimate the probability of future events. Based on a Bayesian approach, it is assumed that probabilities are inferred by combining a priori, potentially subjective, knowledge with factual observations, but the precise neurobiological mechanism remains unknown. Here, we study whether neural encoding centers on subjective posterior probabilities, and data merely lead to updates of posteriors, or whether objective data are encoded separately alongside subjective knowledge. During fMRI, young adults acquired prior knowledge regarding uncertain events, repeatedly observed evidence in the form of stimuli, and estimated event probabilities. Participants combined prior knowledge with factual evidence using Bayesian principles. Expected reward inferred from prior knowledge was encoded in striatum. BOLD response in specific nodes of the default mode network (angular gyri, posterior cingulate, and medial prefrontal cortex) encoded the actual frequency of stimuli, unaffected by prior knowledge. In this network, activity increased with frequencies and thus reflected the accumulation of evidence. In contrast, Bayesian posterior probabilities, computed from prior knowledge and stimulus frequencies, were encoded in bilateral inferior frontal gyrus. Here activity increased for improbable events and thus signaled the violation of Bayesian predictions. Thus, subjective beliefs and stimulus frequencies were encoded in separate cortical regions. The advantage of such a separation is that objective evidence can be recombined with newly acquired knowledge when a reinterpretation of the evidence is called for. Overall this study reveals the coexistence in the brain of an experience-based system of inference and a knowledge-based system of inference.